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Their relationship is pretty twisted. Chillingworth has his suspicions that the ailing young priest is the father of Pearl. Under the guise of helping the minister get better (Chillingworth claims to be a doctor), they become roomies. Chillingworth then has free rein to torture his nemesis. Chillingworth doesn't seem so much interested in revenge more than simply controlling and tormenting Dimmesdale. Both men have this morbid co-dependence thing going on. Chillingworth slowly poisons Dimmesdale and mentally tortures him. For much of the novel, Dimmesdale freely submits to this creepy relationship. Chillingworth doesn't want Dimmesdale to come clean about Pearl because it would end his twisted control over the priest.